2017 · Q68
In triangle ABC, ∠C = 90° and CD is the perpendicular from C to AB. If (CD)²=(BC)⁻²+(CA)⁻², then which one of the following is correct ?
Elementary MathematicsGeometry: Lines, Angles and Triangles
- ABC . CD = AB . CA
- BAB . BC = CD . CA
- CCA² + CB² = 2(AD² + CD²)
- DAB . CD = BC . CA
Explanation
The triangle's area can be written as (1/2)BC·CA and also as (1/2)AB·CD, so BC·CA = AB·CD — option (D), with the strange equation in the stem a red herring. Hence option (D) AB·CD = BC·CA.